Combine chicken, 2 tablespoons olive oil and next 7 ingredients (through pepper flakes) plus a pinch of salt in a bowl. Marinate 15 minutes up to overnight.
Make croutons by heating the remaining 2 tablespoons olive oil in a skillet over medium heat. When the oil shimmers, add the bread and a pinch of red pepper flakes. Cook, stirring occasionally until golden and toasted all over, about 5 minutes. Remove and place on a plate. Wipe pan clean.
Combine salad ingredients in a large bowl and toss.
Combine vinaigrette ingredients in a jar and shake until smooth. Season with salt and pepper to taste. Thin with water if necessary.
Heat the skillet over medium-high heat. Add the chicken in a single layer and cook, stirring once or twice, until the chicken is thoroughly cooked.
Add chicken, croutons, and dressing to the salad and toss. Serve with feta cheese.
